The Linderman reaction mechanism for the isomerization reaction CH_3NC(g) Righta

Question

The Linderman reaction mechanism for the isomerization reaction CH_3NC(g) Rightarrow CH_3CN(g) is CH_3 NC(g) + M(g) Doubleheadarrow^k_1 _k_-1 CH_3 NC^*(g) + M(g) CH_3NC^*(g) Rightarrow^k_2 CH_3CN(g) Under what condition does the steady-state approximation apply to CH_3NC^*? Now consider CH_3NC(g) Rightarrow CH_3CN(g) carried out in the presence of a helium buffer gas. The collision of a CH_3NC molecule with either another CH_3NC or a helium atom can energize the molecule, thereby leading to a reaction. If the energizing reactions involving a CH_3NC molecule and a He atom occur with different rates, the reaction mechanism would be given by CH_3NC(g) + CH_3 NC (g) Doubleheadarrow^k_1 _k_-1 CH_3 NC^* (g) + CH_3 NC (g) CH_3NC(g) + He (g) Doubleheadarrow^k_2 _k_-2 CH_3 NC^* (g) + He(g) CH_3NC^*(g) rightarrow^k_3 CH_3CN(g) Apply the stead-state approximation to the intermediate species, CH_3NC^* (g), to show that d[CH_3CN]/dt = k_3(k_1[CH_3NC]^2 + k_2[CH_3NC][He])/k_-1[CH_3NC] + k_-2[He] + k_3 Show that d[CH_3NC]/dt is first order in CH_3NC when [He] = 0.

Explanation / Answer

By steady state approximation,

d[CH3NC*]/ dt = 0 = k1 [CH3NC]2 - k-1 [ CH3NC*] [CH3NC] + k2 [CH3NC] [He] - k-2[CH3NC*] [He]

0 = k1 [CH3NC]2 - k-1 [ CH3NC*] [CH3NC] + k2 [CH3NC] [He] - k-2[CH3NC*] [He]

k-1 [ CH3NC*] [CH3NC] + k-2[CH3NC*] [He] =  k1 [CH3NC]2 + k2 [CH3NC] [He]

  [ CH3NC*] { k-1 [CH3NC] +  k-2 [He] } = k1 [CH3NC]2 + k2 [CH3NC] [He]

[ CH3NC*] = { k1 [CH3NC]2 + k2 [CH3NC] [He]}/ { k-1 [CH3NC] +  k-2 [He] }

Then,

d[CH3CN]/dt = k3 [ CH3NC* ]

d[CH3CN]/dt =  k3  { k1 [CH3NC]2 + k2 [CH3NC] [He]}/ { k-1 [CH3NC] +  k-2 [He] }

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When [He] = 0 ,

d[CH3CN]/dt =  k3  { k1 [CH3NC]2 }/ { k-1 [CH3NC] }

=  [k3k1/ k-1]  [CH3NC]

= [k3k1/ k-1]  [CH3NC]1

Therefore,

d[CH3CN]/dt is first order in [CH3NC] .

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